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water that connects the drops. Figure 1bshows experimental measurements of thethickness of the two films predicted by thismodel. The two films are separated by ahydrodynamic rim, which has previouslybeen seen both in simulations3 and inexperiments4,11. The measurements used anew form of three-beam interferometry(see legend to Fig. 1b).
For the case investigated, the two filmshave thicknesses of 2555 and 110510 Å.The drops, with their free surfaces far fromthe substrate, have excess chemical potential2rliq
11g/R. For equilibrium with the contin-uous thin film, R must therefore be thesame for all the drops. This implies that thecontact angle increases with a contactradius. But because the film is continuous,the meeting between liquid, vapour andsubstrate, which defines the edge of a drop, is not present, and so a conventionalcontact angle cannot be defined.
It was found in simulations12 that thecontact angle of a drop increases with itsvolume. Water evaporating from the spherical cap is compensated for by con-traction of the contact radius, r, at velocityv41dr/dt. A balance of volumes gives
2prv(h21h1)42arliq11pr2g/R, where a is
the evaporation parameter4. As R is thesame for all drops, it can be shown thatdr/dt is proportional to 1r, as has beenconfirmed experimentally (Fig. 1c, d). Thetypical situation, in which large drops in anarray grow at the expense of the smallerones, is therefore not universally observed,and when the drops coexist with a micro-scopically thin continuous surface layer,they behave differently. I. Leizerson*, S. G. Lipson*, A. V. Lyushnin†*Department of Physics,Technion-Israel Institute of Technology, 32000 Haifa, Israele-mail: [email protected]†Department of Theoretical Physics, Perm StatePedagogical University, Perm 614600, Russia
1. Cazabat, A.-M. Contemp. Phys. 28, 347–364 (1987).
2. Brochard-Wyart, F. Soft Matter Physics 7–44 (Springer,
Berlin, 1995).
3. Sharma, A. & Jameel, A. J. Colloid Interface Sci. 161,
190–208 (1993).
4. Samid-Merzel, N., Lipson, S. G. & Tanhauser, D. S. Phys. Rev. E
57, 2906–2913 (1998).
5. de Gennes, P. G. Rev. Mod. Phys. 57, 325–359 (1985).
6. Israelachvili, J. Intermolecular and Surface Forces 2nd edn
(Academic, San Diego, 1992).
7. Ben-Jacob, E. Nature 343, 523–530 (1990).
8. Ihle, T. & Muller Krumbhaar, H. Phys. Rev. Lett. 70,
3083–3086 (1993).
9. McHale, G., Rowan, S. M., Newton, M. I. & Banerjee, M. K.
J. Phys. Chem. B 102, 1964–1967 (1998).
10.Schafle, C., Bechinger, C., Rinn, B., David, C. & Leider, P.
Phys. Rev. Lett. 83, 5302–5305 (1999).
11.Elbaum, M. & Lipson, S. G. Phys. Rev. Lett. 72,
3562–3565 (1994).
12.Sharma, A. Langmuir 9, 3580–3586 (1993).
Competing financial interests: declared none.
Palaeobotany
Swimming sperm in anextinct Gondwanan plant
The now-extinct plant Glossopteris thatdominated the Southern Hemisphere(Gondwana) during the Permian peri-
od serves as early evidence of continentaldrift1,2, and may be ancestral to the groupof seed plants known as angiosperms3.Here we describe a 250-million-year-oldfossil from Homevale in Queensland, Aus-tralia, of anatomically preserved pollentubes and swimming male gametes fromGlossopteris. The discovery of this simplereproductive system in Glossopteris hasimplications for its phylogenetic relation-ships with extant groups of seed plants(conifers and flowering plants, for exam-ple) and for the evolution of pollinationbiology in general.
Five fossilized pollen tubes are evidentin the pollen chamber of a single ovule,which has been attributed to Glossopterishomevalensis 2 (Fig. 1a, b). They are shortand ovoid, unbranched, and containgametes in several stages of development.Two of the pollen tubes contain a single,immature, spermatogenous cell, two of
396 NATURE | VOL 422 | 27 MARCH 2003 | www.nature.com/nature
vapour, corresponding to a Maxwell con-struction on the chemical potentialmfilm4rliq
11dg/dh, is similar to that betweena liquid and a solid, for example, and a first-order phase transition occurs betweenthem.
The remarkable dendrite-like patternsthat develop during evaporation have beenshown4 to mimic two-dimensional diffu-sion-limited solidification7,8. The late-stagepattern consists of an array of slowly evaporating water drops of widely differingsizes (Fig. 1a). Then, if the contact angle isconstant, coarsening6,9 occurs, as in solidi-fication or cooperative evaporation10, inwhich larger drops acquire fluid fromsmaller ones through vapour transport. Adrop with a smaller radius of contact withthe substrate has a smaller radius of curva-ture, R, and must therefore evaporate fasterowing to the Gibbs–Thomson contribution,2g/R, to its vapour pressure, where g is thesurface tension.
Instead, we have observed that all of thedrops continue to evaporate together, thesmaller ones even evaporating more slowlythan the larger ones. We attribute thisbehaviour to the thin, continuous film of
brief communications
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Figure 1 Behaviour of evaporating water drops on a cleaved mica substrate. a, An array of water drops of widely differing sizes at 0 7C,
photographed at l4546 nm using interference contrast. The first dark ring appears at a thickness of 111 nm. Scale bar, 100 mm.
b, Profile of the interface between the thin and thick films, measured by three-beam interferometry, involving reflections at the
vapour–film interface and both mica surfaces. c, Change in projection radius of drops during 15 min as a function of their radius, for
three different experiments under the same conditions, p/psat40.92050.002. For comparison, on a partially wetted substrate, under
the same p/psat, small drops were swallowed by big ones within 30 s. d, The radius of curvature of drops is independent of their
projection radius. The two lines refer to the same field of drops at different times. Typical error bar is shown on one point.
© 2003 Nature Publishing Group
them each contain a pair of young sperm of immature morphology, and the fifth has been ruptured basally, evidently in the process of dispersing two mature sperm (Fig. 1b–d). No prothallial or sterilecells are evident.
One entire sperm is about 13.9 mmacross, with a helical configuration that represents the multilayered structure uponwhich numerous basal bodies areinserted4,5. This structure is strikingly simi-lar to the flagellate band of many livingpteridophytes6,7, Ginkgo8 and cycads9. Part ofa second sperm also has a spiral structure(Fig. 1c, left arrow). A single line of smalldots occurs at roughly regular intervals(Fig. 1c, d, arrowheads), which are inferredto be basal bodies or the basal plate thatconnects the basal bodies to the flagella(Fig. 1e).
A mature Glossopteris sperm has 37 basalbodies, as determined by optical sectioning.A complete multilayered structure is esti-mated to be about 45 mm long with morethan 50 basal bodies, each at a mean inter-val of 0.57 mm, which form two anticlock-wise gyres (Fig. 1e). By contrast, Ginkgo’s
multilayered structure reaches 300 mm inlength, with 1,000 flagella on three gyres4,whereas that of the cycad Zamia, one of thelargest known plant sperm, is a helical bandof 1,600 mm in length, with six gyres bearing several tens of thousands of flagellaarranged in 8–12 rows at short intervals(0.1 mm; ref. 5).
Glossopteris sperm is therefore moresimilar in size to that of most other vascular plants, including pteridophytes(Botrychium, 10 mm, ref. 6; Lycopodium, 8–10 mm, ref. 7; Equisetum, 19.7 mm, ref. 7),conifers (Torreya, 13–19.5 mm; Pinus, 24 mm; Thuja, 35 mm; ref. 10), gnetophytes(Ephedra, 16 mm; ref. 10) and angiosperms(Hordeum, 11.7 mm; ref. 11). Only theputative sperm found in fossil medullosansare comparable in size to those of cycads, towhich they are often allied, and whosesperm are unusually large9,12.
The pollen tube of Glossopteris differsfrom the highly branched, haustorialpollen tubes of both Ginkgo and cycads, aswell as from the longer, sparsely branchedor unbranched siphonogamous pollentubes of Callistophyton, conifers, bennetti-taleans13 and angiosperms. Glossopterispollen tubes are the simplest known amongvascular plants. They are slightly elongated,unlike in the fossil medullosan ovulePachytesta, where mature sperm inside the pollen protoplast apparently did notelongate to form a pollen tube12 — a typeof structure that has been interpreted as an early stage in the evolution of pollentubes12. Together, our findings indicate thatGlossopteris had a very simple mode ofreproduction that was more similar to thatof cycads and Ginkgo than to those of otherextant seed plants.Harufumi Nishida*, Kathleen B. Pigg†, John F. Rigby‡*Faculty of Science and Engineering, ChuoUniversity, 1-13-27 Kasuga, Bunkyo, Tokyo 112-8551, Japane-mail: [email protected]†Department of Plant Biology, Box 871601, ArizonaState University, Tempe, Arizona 85287-1601, USA‡School of Natural Resource Sciences, QueenslandUniversity of Technology, Box 2434, Brisbane,Queensland 4001, Australia
1. Gould, R. E. & Delevoryas, T. Alcheringa 1, 387–399 (1977).
2. Pigg, K. B. & McLoughlin, S. Rev. Palaeobot. Palynol. 97,
339–359 (1997).
3. Retallack, G. & Dilcher, D. L. Paleobiology 7, 54–67 (1988).
4. Li, Y. et al. Protoplasma 149, 57–63 (1989).
5. Norstog, K. J. Bot. Gaz. 147, 40–46 (1986).
6. Bierhorst, D. W. Morphology of Vascular Plants (Macmillan,
New York, 1971).
7. Gifford, E. M. & Foster, A. S. Morphology and Evolution of
Vascular Plants 3rd edn (Freeman, New York, 1989).
8. Hirase, S. Bot. Mag. Tokyo 10, 325–328 (1896).
9. Ikeno, S. Bot. Mag. Tokyo 10, 367–368 (1896).
10.Chamberlain, C. J. Gymnosperms (Univ. Chicago Press, 1935).
11.Cass, D. & Jensen, W. A. Am. J. Bot. 57, 2–70 (1970).
12.Stewart, W. N. Am. Midl. Natur. 46, 717–742 (1951).
13.Rothwell, G. W. & Stockey, R. A. Botany 2001 Abstracts
25 (2001).
Competing financial interests: declared none.
brief communications
NATURE | VOL 422 | 27 MARCH 2003 | www.nature.com/nature 397
COMMUNICATIONS ARISING
Ecology
Is fertilization efficiencymisleading?
Given the need to increase crop produc-tion in the future while minimizingany associated impact on the environ-
ment, it is important to understand therelationship between global crop produc-tion and fertilization. Tilman et al.1 arguethat fertilization beyond current levels isunlikely to increase crop yields (productionper unit area) as effectively as in the past,due to diminishing returns. However, theirevidence is misleading and does not sup-port their conclusions. Diminishing returnsare not readily apparent on a global scale.
Figure 2 of Tilman et al.1 shows trends inglobal cereal yield and ‘nitrogen-fertiliza-tion efficiency’ (defined as production perunit mass of nitrogen-fertilizer consump-tion) from 1961 to 1996. In the figure,nitrogen-fertilization efficiency plummetsover time while yield climbs relatively lin-early, presumably as fertilization increasedover this period (verified here using datafrom the United Nations Food and Agricul-ture Organization). The figure seeminglysupports the authors’ statements, such as“further increases in nitrogen and phospho-rus application are unlikely to be as effectiveat increasing yields (Fig. 2a) because ofdiminishing returns (Fig. 2b)”. However,the response depicted in their Fig. 2b is a mathematical artefact of the relationshipbetween crop yield and fertilizer-applica-tion rate (mass per unit area), and so doesnot support the authors’ conclusions.
In fertilizing crops, the ideal responsewould be one in which a given increase in fertilizer-application rate leads to a constantincrease in crop yield or, identically, a givenincrease in total fertilizer application leads toa constant increase in production. This idealsystem, in which the effectiveness of fertiliza-tion does not decline as fertilizer use increases,is mathematically represented by p4af&b(where p is the crop production, f is theamount of fertilizer applied, a is the slope ofthe response and b is the production in theabsence of fertilizer).
With this linear response, the nitrogen-fertilization efficiency is represented byp/f4a&b/f, and so is inversely proportionalto f. As f approaches zero, this efficiencyapproaches infinity, and declines as fincreases, tending towards the value of a.This behaviour is quantified by the deriva-tive of fertilization efficiency, namely1b/f 2. Thus, even when a crop shows anideal response to fertilization, fertilizationefficiency declines (Fig. 1).
It seems that global cereal productionhas followed the linear relationshipdescribed above, and has not shown dimin-
Figure 1 Fossil motile sperm in a Late Permian Glossopteris
ovule. Specimens are housed at Chuo University, Tokyo.
a–d, Light micrographs of specimen H397018 E2lat., slide 5.
a, Longitudinal section of the ovule, showing the megagameto-
phyte (below) and three pollen tubes (numbered 1–3) in the pollen
chamber (top). b, Enlarged view of pollen tubes 1 and 2. Top-left
arrows indicate immature sperm in tube 1. Tube 2 (right) is rup-
tured basally and two motile sperm have been released (lower-
right arrows; also evident are the contents of tube 2 and
megagametophyte tissue). c, The two released sperm at higher
magnification; image has been reversed to enhance detail. Arrow,
multilayered helical structure represented by alignment of circular
bodies; arrowheads, line of basal bodies. d, Detail of sperm on
the right in c, showing the basal-body alignment (arrowheads).
e, Schematic diagram of the same sperm, showing the position-
ing of the basal bodies (arrowheads). Scale bars, 100 mm (a, b)
and 5 mm (c, d).
© 2003 Nature Publishing Group
